Asked by victor koskei on Jun 12, 2024
Verified
Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, then P(x = 0) is:
A) 2.5
B) 0.0821
C) 1.5811
D) 0.40
E) 1
Poisson Random Variable
A statistical measure that represents the number of events occurring in a fixed interval of time or space which are independent of each other.
- Calculate the probabilities and statistical parameters (average, dispersion, and deviation) for the Poisson distribution with certain given values.
Verified Answer
MW
Mardrika WebsterJun 19, 2024
Final Answer :
B
Explanation :
Using the Poisson formula, P(x = k) = (λ^k * e^(-λ)) / k!, where λ is the average number of events and k is the specific number of events we want to find the probability of.
In this case, λ = 2.5 and k = 0, so P(x = 0) = (2.5^0 * e^(-2.5)) / 0! = 0.0821.
In this case, λ = 2.5 and k = 0, so P(x = 0) = (2.5^0 * e^(-2.5)) / 0! = 0.0821.
Learning Objectives
- Calculate the probabilities and statistical parameters (average, dispersion, and deviation) for the Poisson distribution with certain given values.
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